Particle Swarm Optimization with non-smooth penalty reformulation for a complex portfolio selection problem

In the classical model for portfolio selection the risk is measured by the variance of returns. It is well known that, if returns are not elliptically distributed, this may cause inaccurate investment decisions. To address this issue, several alternative measures of risk have been proposed. In this contribution we focus on a class of measures that uses information contained both in lower and in upper tail of the distribution of the returns. We consider a nonlinear mixed-integer portfolio selection model which takes into account several constraints used in fund management practice. The latter problem is NP-hard in general, and exact algorithms for its minimization, which are both effective and efficient, are still sought at present. Thus, to approximately solve this model we experience the heuristics Particle Swarm Optimization (PSO). Since PSO was originally conceived for unconstrained global optimization problems, we apply it to a novel reformulation of our mixed-integer model, where a standard exact penalty function is introduced.Portfolio selection, coherent risk measure, fund management constraints, NP-hard mathematical programming problem, PSO, exact penalty method, SP100 index's assets.

Estimation of Econometric Models by Risk Minimization: A Stochastic Quasigradient Approach

The paper presents a risk minimization approach to estimate a flexible form that meets a priori restrictions on slope and curvature by means of constraints on both the estimated parameters and the function values. The resulting constrained risk minimization combines parametric and nonparametric estimation and contains integrals and implicit constraints. Within econometrics, simulation has become a common tool to solve problems of this kind. However, it appears that in our case, the simulation approach only applies when the model is linear in parameters, has simple constraints on parameters and a quadratic risk function. To deal with other cases, we use a stochastic optimization technique known as the stochastic quasi-gradient method for stationary and nonstationary problems with Cesaro averaging. This method is also applicable to an expanding series of random observations, and produces asymptotically (weakly) convergent estimates

On the ERM Principle with Networked Data

Networked data, in which every training example involves two objects and may share some common objects with others, is used in many machine learning tasks such as learning to rank and link prediction. A challenge of learning from networked examples is that target values are not known for some pairs of objects. In this case, neither the classical i.i.d.\ assumption nor techniques based on complete U-statistics can be used. Most existing theoretical results of this problem only deal with the classical empirical risk minimization (ERM) principle that always weights every example equally, but this strategy leads to unsatisfactory bounds. We consider general weighted ERM and show new universal risk bounds for this problem. These new bounds naturally define an optimization problem which leads to appropriate weights for networked examples. Though this optimization problem is not convex in general, we devise a new fully polynomial-time approximation scheme (FPTAS) to solve it.Comment: accepted by AAAI. arXiv admin note: substantial text overlap with arXiv:math/0702683 by other author